Talk:Gibbs phenomenon

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Teorth, try to keep formulas as short as possible. For example, on one of my computers, when I viewed the page in its previous state, the formula for the sum could not fit alongside the pictures and was pushed below them, making an ugly enormous gap in the page. The same holds for the formulas in the "Formal mathematical description of the phenomenon" — try to make them look aesthetic even with a narrow window.

Oh, and I think the half error was on the other side — please check my calculations. Gadykozma 13:13, 28 Oct 2004 (UTC)

OK, I've split the longest equation into three pieces; feel free to truncate the others as necessary. Regarding all the factors of 2, I think I've fixed them all now... Terry 18:05, 28 Oct 2004 (UTC)


Doesn't the overshoot remain (though with zero width) in the infinite limit? If so, then the arguments in the second paragraph should be changed since they are false.74.98.54.54 19:12, 12 May 2007 (UTC)

No the overshoot does not exist at all in that case. "An infinite sum of continuous functions can be discontinuous" is correctly stated. Cuddlyable3 10:16, 14 May 2007 (UTC)
The fact that "An infinite sum of continuous functions can be discontinuous" is correct and irrelevant, and more over it doesn't follow from this fact that the infinite sum "does not exhibit the Gibbs phenomenon". In fact, the described phenomenon is a property of the sequence of partial sums and not of it's (pointwise) limit, so there no meaning to the statement that the limit function "does not . It doesn't belong in this article, and if it does, it cannot be phrased by assigning a true or false value to the statement that the limit function "exhibits the Gibbs phenomenon" because this sentence does not accept one of these two values. Hadaso (talk) 09:24, 9 December 2007 (UTC)


[edit] Square Wave Definition

The Description section defines the square wave function this way: "More precisely, this is the function f which equals π / 4 between 2nπ and (2n + 1)π and − π / 4 between 2(n + 1)π and 2(n + 2)π for every integer n; thus this square wave has a jump discontinuity of height π / 2 at every integer multiple of π."

I don't think that's quite right. Shouldn't it be "... π / 4 between 2nπ and (2n + 1)π and − π / 4 between (2n + 1)π and 2(n + 1)π" ? DRE 15:49, 13 March 2007 (UTC)

Looks like it. I've changed it. Michael Hardy 21:52, 13 March 2007 (UTC)

[edit] Image-compression example

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The Free Image Search Tool (FIST) may be able to locate suitable images on Flickr and other web sites.